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This article is cited in 5 scientific papers (total in 5 papers)
Solutions of $p$-adic string equations
V. S. Vladimirov
Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia
Abstract:
We review several purely mathematical results concerning boundary value problems for nonlinear pseudodifferential equations for $p$-adic closed and open strings in the tree approximation in the case $d=1$. For the solutions of these problems, we present formulas establishing the relations between the numbers of their zeros, the multiplicities of the zeros, and the numbers indicating how many times the solutions change sign.
Keywords:
$p$-adic string
DOI:
https://doi.org/10.4213/tmf6631
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English version:
Theoretical and Mathematical Physics, 2011, 167:2, 539–546
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Received: 13.10.2010
Citation:
V. S. Vladimirov, “Solutions of $p$-adic string equations”, TMF, 167:2 (2011), 163–170; Theoret. and Math. Phys., 167:2 (2011), 539–546
Citation in format AMSBIB
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http://mi.mathnet.ru/eng/tmf6631https://doi.org/10.4213/tmf6631 http://mi.mathnet.ru/eng/tmf/v167/i2/p163
Citing articles on Google Scholar:
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This publication is cited in the following articles:
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V. S. Vladimirov, “Nonexistence of solutions of the $p$-adic strings”, Theoret. and Math. Phys., 174:2 (2013), 178–185
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I. V. Volovich, V. Zh. Sakbaev, “Universal boundary value problem for equations of mathematical physics”, Proc. Steklov Inst. Math., 285 (2014), 56–80
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Dragovich B. Khrennikov A.Yu. Kozyrev S.V. Volovich I.V. Zelenov E.I., “P-Adic Mathematical Physics: the First 30 Years”, P-Adic Numbers Ultrametric Anal. Appl., 9:2 (2017), 87–121
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Kh. A. Khachatryan, “On the solubility of certain classes of non-linear integral equations
in $p$-adic string theory”, Izv. Math., 82:2 (2018), 407–427
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Kh. A. Khachatryan, A. S. Petrosyan, M. O. Avetisyan, “Voprosy razreshimosti odnogo klassa nelineinykh integralnykh uravnenii tipa svertki v $\mathbb {R}^n$”, Tr. IMM UrO RAN, 24, no. 3, 2018, 247–262
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